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1 Improving Access to Language In Mathematics Emily Fagan & Amy Brodesky, EDC Welcome! Please complete the warm-up (HO 1)

Language in the Math Classroom

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Language in the Math Classroom; A Workshop for Mathematics and Special Educators focuses on ways in which middle- grades math and special education teachers can support students with the language demands of the middle grades math classroom. This presentation is part of a broader workshop for educators. More information at http://middlegradesmath.org

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Improving Access to Language In Mathematics

Emily Fagan & Amy Brodesky, EDC

Welcome! Please complete the warm-up (HO 1)

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Our PD Projects Addressing Accessibility in Mathematicshttp://edc.org/accessMath/

Mathematics Improvement Toolkithttp://www.mgforum.org/(June or July 2009)

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Our PD Goals for Language in MathBuild teachers’ knowledge of…

the kinds of language demands in math lessons

common difficulties that students with learning disabilities

strategies for addressing these difficulties ways to plan accessible math lessons that

incorporate active language strategies

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Lessons Learned about PD on Language Strategies for Math

Tends to be a motivating and engaging topic for math teachers & special educators Helpful to unpack language demands & difficulties

Provides an opportunity for special educators to share expertise and to foster collaboration between special educators & math teachers

Needs to go beyond “activities” to integrating language strategies into math instruction

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Session Agenda

1. Language Demands in Mathematics2. Sample Lesson3. Writing in Math4. Math Vocabulary5. Planning for Language Accessibility

We hope you will leave with PD ideas to use with teachers in your schools/districts.

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#1: Examine the Language Demands in Mathematics Lessons

In this section, we will: Discuss the kinds of language demands in

mathematics lessons Learn about the complexities of reading in

mathematics Consider language challenges for students

with disabilities

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Communication Standard:Goals for Students Organize and consolidate their mathematical

thinking through communication;

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

Analyze and evaluate the mathematical thinking and strategies of others;

Use the language of mathematics to express mathematics ideas precisely.

Source: Principles and Standards for School Mathematics (NCTM), 2002

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Types of Language Demands

Receptive Reading Listening

Expressive Writing Speaking

Examples for students with disabilities:Reading: Decoding; ComprehensionListening: Auditory ProcessingWriting: Organizing ideas in writingSpeaking: Expressing ideas orally

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Student’s Perspective

Source: “Faking It” by C. Lee and R. Jackson

“When I am listening or reading a word problem, I sometimes leave out or reverse important information. When I am struggling through the words, I lose the meaning of the problem.”

Source: “Faking It” by C. Lee and R. Jackson

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Reading in Mathematics Class

Compare:FICTION

Dorothy lived in the midst of the great Kansas prairies, with Uncle Henry, who was a farmer, and Aunt Em, who was the farmer's wife. Their house was small, for the lumber to build it had to be carried by wagon many miles.

Baum, L. F. p.1

MATHEMATICS TEXTThe sum of two numbers having the same sign can be found by adding their absolute values, the answer having the same sign as the numbers.

What differences do you notice?

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What’s different about reading mathematics texts?

Conceptually dense

Not just words – also symbols, tables, graphs and diagrams

Not just left to right-different directions

Different symbols are used to describe the same process Multiplication *, x, (), ●

Decoding symbols is different from decoding words. Symbols are like “sight words.”

Barton and Heidema, 2002, p. 1

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#2: Use a Sample Lesson for Professional Development

In this section, we will: watch and discuss a video of a lesson that

involves reading, discussing, and writing about abstract equations

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PD Simulation: View and Discuss a Video

Goals: Provide examples of strategies in action Provide a shared experience to

generate discussion

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Mathematics Lesson in Video Reviews vocabulary from their curriculum

Factored Form: (x+1)(x+4) Expanded Form: x2 + 4x + 1

Uses an area model for equations Uses Algebra Tiles (manipulatives)

x2 x

Algebra Tiles

1

HO 2A: Lesson

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Video: BackgroundStudents Six 8th grade students, including students with disabilities

and English Language Learners Identified for additional support because they were having

difficulties in regular mathematics class As a group, these students tend to be reluctant to participate

Teacher Title I Mathematics Coach Co-teaches 8th grade mathematics class AND provides

additional mathematics support to these students

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As You Watch, Keep in Mind…

One teacher, one day An example to spark discussion

Focus Question What kinds of strategies does the teacher

use to make the language of the mathematics accessible?

HO 2: Video Notes

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Discuss: What kinds of difficulties did the

students have? What strategies did the teacher use to

make the language of mathematics more accessible?

What strategies do you find helpful for encouraging reluctant students to participate?

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#3: Focus on Writing Strategies for Mathematics Class

In this section, we will simulate a professional development experience in which teacher participants:

Write a response to a mathematics problem Examine student work samples Discuss writing strategies

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Why Write in Mathematics?

Writing can help students to: build understanding of mathematics organize and clarify ideas deepen their thinking communicate coherently and clearly remember mathematics content

Writing has many benefits. But, it also poses barriers for some students.

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PD Simulation:Looking at Student Work

What do teachers do? Write a response to a math problem. Discuss their experiences. Analyze the problem from accessibility

lens. Examine student work samples.

HO 3: Jumping Jacks

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Analyze Problem from an Accessibility Lens What are the math goals?

What are the demands on students?ConceptualLanguageVisual-Spatial

What potential difficulties would you anticipate for students?

HO 3 Jumping Jacks

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Looking at Student Work (LASW) Key Questions

1. What do you observe about the student’s math understanding?

2. What do you observe about the student’s writing?

HO 4 LASW Tool

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LASW Directions

1. Look at the samples from three 6th graders.

2. Then focus on Student Z. Write notes on your LASW Tool.

3. In small groups, discuss Student Z’s work. Strengths and Difficulties Questions and Strategies

HO 5 Students X, Y, Z

HO4 LASW Tool

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Discuss Observations, Questions & Strategies

Z

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Discuss Observations, Questions & Strategies

X

Y

Z

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Teachers Discuss Writing Strategies for Math Look over the list of strategies. What strategies might be helpful to your

students, especially those with disabilities? Why?

What’s one strategy that you currently use? How do you use it?

HO6 Writing Strategies

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#4: Expand Teachers’ Repertoires of Vocabulary Strategies

In this section, we will examine pd activities designed to:

View video to spark reflection & discussion Explore vocabulary challenges Provide & practice strategies

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Vocabulary is Everywhere

Receptive Reading Listening

Requires: Recognizing vocabulary Understanding

vocabulary

Expressive Writing Speaking

Requires: Recalling vocabulary Applying vocabulary

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Complexities of Mathematics Vocabulary

Some terms… are shared with everyday English but have distinct

meanings in mathematics Right, volume, expression

sound like everyday English words Sum and Some

have more than one meaning in mathematics Square, round

are related and often confused Mean and median

Source: Rubenstein, R. 2007

HO 7: Math Vocabulary

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Vocabulary in the Geometry & Data Strands

2 Video Clips: 7th grade class: Data 6th grade class: Geometry

Video Reminder One teacher/one day An example to spark reflection and discussion

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As You Watch, Keep in Mind

Focus Question What strategies does each teacher use

to help students to understand the vocabulary in the lesson?

HO 8: Video Notes

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Discuss with a Partner What strategies did you observe the

teachers use to help students understand vocabulary?

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Sample Strategy: Visual Definitions

Polygons Not Polygons

Generate examples of shapes that are and are not the vocabulary word.

Ask students to come up with a definition for the word.

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Vocabulary 4-Block Strategy

Median

The middle value in a set of ranked

data

1, 1, 4, 6, 7, 10,21

Median sounds like medium --the middle

Don’t forget to put the numbers from

smallest to largest!

This strategy helps students build understanding by organizing information about a term.

HO 9 Vocab. 4-block

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Discussion Questions for Teachers

Reflect on Your Experience In what ways did you find filling the 4-block to be

helpful to you? Were some blocks harder to fill in than others?

Discuss Ways for Using the 4-Block with Students Which words would you want your students to use? After students complete the cards, what are ways

they could continue to use them in active ways?

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“I Have, Who Has” Activity: Demo

Who has a five-sided polygon?

1. First player asks question

I have a pentagon.

Who has a 90◦ angle?

2. Player with matching word responds and then asks next question.

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“I have, Who has”DirectionsTo Get Started:1. Each person gets one or more cards.2. Talk with a partner about the meanings of the

vocabulary words on your cards.Play the Game:3. One person begins by reading the question only.4. The person who has the statement that matches,

reads the statement.5. That same person then reads the question on his/her

card.6. Play continues until all the cards have been used.

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Discussion Questions for Teachers

How do you or would you use the “I have, who has” vocabulary activity with students?

How would you make it more accessible to students with learning disabilities?

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Things to Keep in Mind: Vocabulary in Mathematics

Identify critical terms and phrases (5-7 is better than 20-25).

Students need many opportunities to speak, read, write and listen to mathematics vocabulary.

Sometimes the words that prevent students from solving a task are not mathematical terms.

Handout 10: Analyzing a Math Task

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#5: Provide Planning Processes and Tools

In this section, we will: Consider the challenges for teachers in addressing

language and vocabulary in instruction Share ideas for facing these challenges Examine sample planning processes and tools

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Common Challenges Vocabulary strategies, such as word walls

and index card dictionaries, are created but then are not used in active or ongoing ways

Math teachers may lack knowledge of language strategies and/or ways to incorporate strategies in lessons

Limited time in math lessons

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Suggestions for Math Supervisors Incorporate language and vocabulary

planning as a regular feature of lesson planning

Provide a structure for planning Encourage collaboration to share ideas

and resources Set and clarify expectations for

incorporating language strategies

Handout 11: Sample Planner

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Share Your Experience What are your suggestions for

helping mathematics teachers with language and vocabulary strategies?

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Closing

Questions and Comments

[email protected]@edc.org

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Optional Slides

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Suggestions: Using LASW in PD Caution: teachers may jump to strategies. Use an

organizer and provide ample time to discuss student’s strengths and difficulties first.

Consider questions to ask to gather more information before choosing strategies

Emphasize aligning strategies with math goals and student

Consider ways to build on student’s strengths to help address difficulties

Provide work from a range of learners